A tower is 50 meters high. Its shadow is x meters shorter when the sun’s altitude is 45° than when it is 30°. The value of x in metres is
50(√3 - 1)
Let the height of the tower be h = 50 meters.
When the sun's altitude is 30°, the shadow length is \(l_1 = \frac{h}{\tan 30^\circ} = \frac{50}{\frac{1}{\sqrt{3}}} = 50\sqrt{3}\) meters.
When the sun's altitude is 45°, the shadow length is \(l_2 = \frac{h}{\tan 45^\circ} = \frac{50}{1} = 50\) meters.
The difference in shadow lengths is \(x = l_1 - l_2 = 50\sqrt{3} - 50 = 50(\sqrt{3} - 1)\) meters.
Therefore, the value of x is 50(√3 - 1) meters.
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